Positive solutions for a class of boundary value problems on time scales

Authors:
Meiqiang Feng;Xuemei Zhang;Weigao Ge
Affiliations:
Department of Fundamental Sciences, Beijing Information Technology Institute, Beijing 100101, PR China and Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China;Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, PR China;Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China
Venue:
Computers & Mathematics with Applications
Year:
2007

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Abstract

By obtaining intervals of the parameter @l, this paper is concerned with the existence and nonexistence of positive solution of the second-order nonlinear dynamic equation on time scales -[p(t)x^@D(t)]^@?+q(t)x(t)=@lw(t)f(t,x),@ax(@r(a))-@bx^[^@D^](@r(a))=0,@cx(b)+@dx^[^@D^](b)=0 for t@?[a,b]@?T, where T is a time scale, @a=0,@c=0,@b0,@d0 with @a+@c0. The arguments are based upon fixed point theorems in a cone.